Implement matrix multiplication function

This function performs matrix multiplication on two valid matrices, raising ValueErrors for invalid structures or incompatible sizes.

Author: ArsiyaTasleem90250

matrix/matrix_diagonal_sum.py

@@ -0,0 +1,63 @@
+"""
+Matrix Multiplication Algorithm
+
+This function performs matrix multiplication on two valid matrices.
+It follows the mathematical definition:
+If a is an m x n matrix and b is an n x p matrix,
+then their product c is an m x p matrix.
+
+Raises:
+    ValueError: if matrices have invalid structure or incompatible sizes.
+
+Sources:
+    https://en.wikipedia.org/wiki/Matrix_multiplication
+
+Examples:
+    >>> A = [[1, 2], [3, 4]]
+    >>> B = [[5, 6], [7, 8]]
+    >>> matrix_multiply(A, B)
+    [[19, 22], [43, 50]]
+
+    >>> matrix_multiply([[1, 2, 3]], [[4], [5], [6]])
+    [[32]]
+
+    # Invalid structure
+    >>> matrix_multiply([[1, 2], [3]], [[1, 2]])
+    Traceback (most recent call last):
+    ...
+    ValueError: Invalid matrix structure
+
+    # Incompatible sizes
+    >>> matrix_multiply([[1, 2]], [[1, 2]])
+    Traceback (most recent call last):
+    ...
+    ValueError: Incompatible matrix sizes
+"""
+
+def matrix_multiply(a: list[list[float]], b: list[list[float]]) -> list[list[float]]:
+    if not _is_valid_matrix(a) or not _is_valid_matrix(b):
+        raise ValueError("Invalid matrix structure")
+
+    rows_a = len(a)
+    cols_a = len(a[0])
+    rows_b = len(b)
+    cols_b = len(b[0])
+
+    if cols_a != rows_b:
+        raise ValueError("Incompatible matrix sizes")
+
+    result = [[0.0 for _ in range(cols_b)] for _ in range(rows_a)]
+
+    for i in range(rows_a):
+        for j in range(cols_b):
+            for k in range(cols_a):
+                result[i][j] += a[i][k] * b[k][j]
+
+    return result
+
+
+def _is_valid_matrix(m: list[list[float]]) -> bool:
+    if not isinstance(m, list) or not m:
+        return False
+    first_length = len(m[0])
+    return all(isinstance(row, list) and len(row) == first_length for row in m)